12 Labours tools for developing Functional Tissue Units

TL;DR

Multiscale physiology modelling requires modular, physically consistent representations of Functional Tissue Units (FTUs) that preserve energy and mass across cellular subsystems. The paper adopts port-Hamiltonian and PH-DAE representations for cells and provides a compositional framework for linking them while ensuring passivity and energy balance, including formulas such as $E dx/dt = (J-R) Q x$ and $y = B^T Q x$ with grad H(x) = E^T J Q x. It introduces FTUUtils (Python) and FTUWeaver (browser) to construct FTU graphs, load PH-DAEs, and specify networks, yielding a self-contained JSON composition for simulation. This framework enables modular, physically grounded modelling of tissue units and their interactions, with planned analytical and model order reduction techniques to facilitate scalable simulations.

Abstract

A brief introduction of the technical approach to model FTUs as an aggregate of cells, whose state transition dynamics are mathematically represented as port-hamiltonians or Differential Algebraic equations is presented. A python library and browser based tool to enable modellers to compose the FTU graph, specify the cellular equations and the interconnection between the cells at the level of physical quantities they exchange consistent with the technical approach is discussed.

Figures (10)

• Figure 1: Spatial scales of various physiological structures and imaging modalities through which these structures could be investigated. A example mapping of these structures for kidneys. Acronyms: CT, computed tomography; MRI, magnetic resonance imaging; OCT, optical coherence tomography; PAS, Periodic Acid-Schiff; H&E, hematoxylin and eosin; AF, autofluorescence. Adapted from Figure 1 of Jain2023 and Figure 4 of Borner2022.
• Figure 2: (1), (2): Composition and 3D reconstruction of normal and infarcted myocardium. [B–E] Zoom-ins for the white boxes in (A) display representative microstructural features. (F) Reconstructed myocytes from the image stack. Myocytes were colored individually. The black line segments mark the edges and corners of the image stack. (G) Reconstructed non-myocyte contributors to the myocardium with ES in blue, vessels in red, fibroblasts in cyan, and myofibroblasts in yellow. The ES visualization is clipped in half for visibility of other tissue constituents. (3) Primary adult human retina section j and retinal organoid sections from different timepoints k–n. (4) FTU segmentations by HubMAP project (a) Glomerulus in the kidney. b Crypt in the large intestine (top: perpendicular cross-section, bottom: lengthwise cross-section). c Alveolus in the lung. d Glandular acinus in the prostate. e White pulp in the spleen. (1), (2) reproduced figure 1 and 2 of Greiner2022, (3) reproduced figure 1 of Wahle2023, (4) reproduced figure 2 of Jain2023b
• Figure 3: Schematic of the process of identifying a representative region to model a sFTU, extracting cell type information, creating cell type blocks (C,D,E) and creating a graph based representation for each block. Matrix effects can be encoded in the graph via edge annotations that characterise the influence of the matrix or via pseudo cells that capture the local influence of the matrix and integrate them with the grpah (G). Image credit. Dr Mark Trew.
• Figure 4: RLC circuit with a voltage source with potential $V$, state variables $q$-charge stored in the capacitor and $\phi$-magnetic flux in inductor. Its bondgraph, circuit diagram, state space and port-hamiltonian representation.
• Figure 5: Schematic of energy flow through interconnected systems (nodes) and the concept of passivity that requires the energy that flows out of the system is less than or equal to the energy that flows into the system. The composite system receives external inputs from a subset of nodes and outputs/communicates with the environment through anothet subset of nodes (not mutually exclusive from the ones from which it recieves input).